Existence of small oscillations at zeros of brownian motion

Frank B. Knight

Séminaire de probabilités de Strasbourg (1974)

  • Volume: 8, page 134-149

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Knight, Frank B.. "Existence of small oscillations at zeros of brownian motion." Séminaire de probabilités de Strasbourg 8 (1974): 134-149. <http://eudml.org/doc/113004>.

@article{Knight1974,
author = {Knight, Frank B.},
journal = {Séminaire de probabilités de Strasbourg},
language = {eng},
pages = {134-149},
publisher = {Springer - Lecture Notes in Mathematics},
title = {Existence of small oscillations at zeros of brownian motion},
url = {http://eudml.org/doc/113004},
volume = {8},
year = {1974},
}

TY - JOUR
AU - Knight, Frank B.
TI - Existence of small oscillations at zeros of brownian motion
JO - Séminaire de probabilités de Strasbourg
PY - 1974
PB - Springer - Lecture Notes in Mathematics
VL - 8
SP - 134
EP - 149
LA - eng
UR - http://eudml.org/doc/113004
ER -

References

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  1. 1. A. Dvoretzky, On the oscillation of the Brownian motion process, Israel Jour. Math. Vol. 1, #4 (1963), 212-214. Zbl0211.48303MR164378
  2. 2. K. Ito and H.P. McKean, Jr., Diffusion processes and their sample paths, Springer, Berlin, 1965. Zbl0127.09503
  3. 3. F. Knight, Random walks and a sojourn density process of Brownian motion, Trans. Amer. Math. Soc.109(1963), 56-86. Zbl0119.14604MR154337
  4. 4. F. Knight, Brownian local times and taboo processes, Trans. Amer. Math. Soc.143(1969), 173-185. Zbl0187.41203MR253424
  5. 5. P. Levy, Théorie de l'addition des variables aleatoires, Gauthier-Villars, Paris, 1954. Zbl0056.35903MR586767JFM63.0490.04
  6. 6. P. Lévy, Processus stochastiques et mouvement Brownien, Gauthier-Villars, Paris, 1948. Zbl0034.22603MR29120
  7. 7. B.B. Mandelbrot, Renewal sets and random cutouts, Z. Wahrscheinlichkeitstheorie verw. Geb.22(1972), 145-157. Zbl0234.60102MR309162
  8. 8. H.P. McKean, Jr., Stochastic integrals, Academic Press, New York, 1968. Zbl0191.46603
  9. 9. S. Orey and S.J. Taylor, How often on a Brownian path does the law of the iterated logarithm fail? To appear. Zbl0292.60128MR359031
  10. 10. L. Shepp, Covering the line with random intervals, Z. Wahrscheinlichkeitstheorie verw. Geb.23(1972), 163-170. Zbl0238.60006MR322923
  11. 11. M. Silverstein, A new approach to local times, J. Math. Mech.17(1968), 1023-1054. Zbl0184.41101MR226734
  12. 12. S.J. Taylor, Exact asymptotic estimates of Brownian path variation, Duke Jour.39(1972), 219-241. Zbl0241.60069MR295434

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